I first learned about the curlique fractal here: http://bit-player.org/bph-publications/SciAm-1984-02-Hayes-turtle.pdf Here's a javascript version to play with: https://www.khanacademy.org/computer-programming/spirals/1023512142 On Wed, Feb 21, 2018 at 4:01 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Is the "temperature" simply the maximum distance from the origin?
No, it's T = 1/ln(2L/(2L-H)), where L is the length of the curve and H is the length of the convex hull. http://mathworld.wolfram.com/Temperature.html
Can you say more about the dependence on the number of steps? Is it possible that we would see a higher temperature for e×γ if we let it go longer?
It looks like the convex hull approaches a circle, so H is bounded but L is not, which appears to me to mean that T should approach infinity. "The value s=e×γs=e×γ reaches a maximum temperature of 2433.73 at 460024 steps. For awhile, this has been the highest achieved temperature." I don't understand how it can be claimed to have a maximum temperature under this definition. Maybe the total length is normalized to 1? -- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com